Strengthened Bell Inequalities for Entanglement Verification

Details Strengthened Bell Inequalities for Entanglement Verification Strengthened Bell Inequalities for Entanglement Verification

2009-08-03

arxiv.org/abs/0908.0267v2

Phys. Rev. A 80, 034302 (2009)

Physics

Quantum Physics

This submission, together with the previous one, supersedes arXiv:0806.4165

Scientific paper

Bell inequalities were meant to test quantum mechanics vs local hidden variable models, but can also be used to verify entanglement. For entanglement verification purposes one assumes the validity of quantum mechanics as well as quantum descriptions of one's measurements. With the help of these assumptions it is possible to derive a strengthened Bell inequality whose violation implies entanglement. We generalize known examples of such inequalities by relating the expectation value of the Bell operator to a particular quantitative measure of entanglement, namely the negativity. Moreover, we obtain statistics illustrating the fact that violating a given (strengthened or not) Bell inequality is a much more rare feat for a quantum state of two qubits than it is to be entangled.

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